First-Principle Homogenization Theory for Periodic Metamaterials

TL;DR

This paper develops a first-principles homogenization theory for periodic metamaterials, providing accurate effective parameters and clarifying the role of spatial dispersion and magnetoelectric effects beyond standard models.

Contribution

It introduces a new homogenization approach that overcomes limitations of existing methods, including closed-form expressions and insights into spatial dispersion and magnetoelectric coupling.

Findings

Effective parameters derived from first principles.

Spatial dispersion effects are significant even at long wavelengths.

Magnetoelectric coupling can occur in symmetric inclusions.

Abstract

We derive from first principles an accurate homogenized description of periodic metamaterials made of magnetodielectric inclusions, highlighting and overcoming relevant limitations of standard homogenization methods. We obtain closed-form expressions for the effective constitutive parameters, pointing out the relevance of inherent spatial dispersion effects, present even in the long-wavelength limit. Our results clarify the limitations of quasi-static homogenization models, restore the physical meaning of homogenized metamaterial parameters and outline the reasons behind magnetoelectric coupling effects that may arise also in the case of center-symmetric inclusions.